Question

6 7 8 9 10 TIME REMAINING 56:32 A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x + 6y = 7.50 10x + 5y = 8.75 What is the cost of one apple? $

Answer 1

Given:
let x = apples
let y = oranges

Equation 1: 6x + 6y = 7.50
Equation 2: 10x + 5y = 8.75

Equation 1 - Equation 2
6x + 6y = 7.50
- (10x + 5y = 8.75)
-4x+ y = -1.25
y = -1.25 + 4x

6x + 6y = 7.50
6x + 6(-1.25 + 4x) = 7.50
6x - 7.50 + 24x = 7.50
30x = 7.50 + 7.50
30x = 15
x = 15/30
x = 1/2 or 0.50 cost of one apple

y = -1.25 + 4x
y = -1.25 + 4(0.50)
y = -1.25 + 2
y = 0.75 cost of one orange

6x + 6y = 7.50
6(0.50) + 6(0.75) = 7.50
3 + 4.5 = 7.50
7.50 = 7.50

10x + 5y = 8.75
10(0.5) + 5(0.75) = 8.75
5 + 3.75 = 8.75
8.75 = 8.75